A unifying view to fractional modeling

We clarify in a consistent mathematical way the relationship between the well-known long-range dependence and self-similarity in its different appearances namely the exact second-order and the asymptotic second-order self-similarity. We prove that long-range dependence equals asymptotic second-order self-similarity so that both expressions can be used interchangeably. In contrast to long-range dependence exact second-order self-similarity has a fixed structure for all its correlation coefficients. This is an important fact because there is a large impact of short-range correlation coefficients to multimedia models, that would be neglected with exact second-order self-similar models